"I lie awake, staring out at the bleakness of Megadon. City and sky become one, merging into a single plane, a vast sea of unbroken grey. The Twin Moons, just two pale orbs as they trace their way across the steely sky. I used to think I had a pretty good life here, just plugging into my machine for the day, then watching Templevision or reading a Temple Paper in the evening.

My friend Jon always said it was nicer here than under the atmospheric domes of the Outer Planets. We have had peace since 2062, when the surving planets were banded together under the Red Star of the Solar Federation. The less fortunate gave us a few new moons.

I believed what I was told, I thought it was a good life, I thought I was happy. Then I found something that changed it all..."

WHY IS NEIL PEART SO VAGUE? WHERE IS THE SOLAR FEDERATION?!?!

It sounds like it's on Earth, in our own Solar System, but there could also be the possibility of another Earth-like planet, in another galaxy, with human-like alien life and all sorts of tech stolen from Earth... AND that the SF is actually a group of alien races, of which the Syrinx are chief among them...

There are those who believe that life here began out there… far across the universe, with tribes of humans who may have been the forefathers of the Egyptians or the Toltecs or the Mayans. Some believe that there may yet be brothers of man who even now fight to survive somewhere beyond the heavens.

When people began to multiply on the face of the ground, and daughters were born to them, the sons of God saw that they were fair; and they took wives for themselves of all that they chose. Then the Lord said, “My spirit shall not abide in mortals forever, for they are flesh; their days shall be one hundred twenty years.” The Nephilim were on the earth in those days—and also afterward—when the sons of God went in to the daughters of humans, who bore children to them. These were the heroes that were of old, warriors of renown.
— Genesis 6:1–4,

Answer: It is wherever you want it to be. It is a work of fiction. Use your imagination and locate it anywhere you want.

Similar to how the details of the ending are ambiguous, so are many such insignificant details as this. This is Neil Peart, not Tolkien. 2112, not The Lord Of The Rings. If you want the best storytelling possible, you go for a great fictional novel. If you want the best storytelling possible in a rock song, you'll probably have to lower your standards a bit.

Do we even know if 2112 is supposed to be 2112AD? It's just a date number, could refer to anywhere at anytime...

A great many science fiction stories have future human societies and empires that use different calendars and dating systems, like in Frank Herbert's Dune and Isaac Asimov's Foundation series. They exist tens of thousands of years in the future.